# Modeling and Probabilistic Analysis of Slope Stability

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Today, the use of statistical and probabilistic methods in engineering sciences has been expanded, especially civil engineering, where the problem-solving data, including relations and parameters due to the various unknown factors, is always associated with uncertainty. Simulation methods have also been expanded, including methods such as Monte Carlo, Advanced Monte Carlo and Point Estimation.

Considering these cases, there was a vacancy in powerful software in the field of geotechnical engineering that has the ability to analyze issues in statistical and probabilistic ways.

The problem was solved to a large extent by collecting a set of specialized mining engineering software.

One of the most popular software is the following:

The Phase2 software, which is a two-dimensional finite element software, and in addition to definitive analysis of the problems using a definitive method has high capability of probability analysis of geotechnical problems such as tunnel engineering, drilling, analysis of slopes, and water-flow seepage analysis.

The Slide software, which is a two-dimensional limiting equilibrium software, and is capable of solving the slope stability problems in a deterministic and probabilistic way.

The Swedge software, which is used to analyze the stability of wedges formed in drillings.

Probabilistic Methods

In probabilistic methods, the software generates random samples using the defined distributed function for the random variable.

Then, for each produced sample, it analyzes the problem and yields an output in which, the accuracy of the problem depends to a large extent on the number and distribution of the samples.

To utilize probabilistic methods for simulation problems, it is necessary to understand statistical concepts, especially the recognition of distribution functions in proportion to the problem requirement and the sampling method.

The most widely used distribution functions in geotechnical engineering, include beta, triangular, normal, and logarithmic normal functions.

Simulation methods:

Among the most widely used simulations in geotechnical problems that are flexible and highly precise, the following can be mentioned:

• Point estimation method
• Latin hypercube method
• Monte Carlo method

Some of the most important advantages of using probabilistic methods in simulating and solving problems are:
• Considering the uncertainties of the problem that arise from the lack of understanding of the inputs of the problem and etc.
• The answer to the problem, which is in the form of the probability of an occurrence or incident, and is not a deterministic and definite answer.
• Possibility to examine the sensitivity of the problem to input changes and determine the important and influential parameters using sensitivity analysis or regression analysis.

Monte Carlo Simulation

• Monte Carlo simulation is one of the best numerical methods among simulation methods.
• It is a method for generating random samples based on the recognition of the numerical test distribution function
• The Monte Carlo method is based on the random number generation.
• Due to their reliance on repetitive calculations and random or false random numbers, Monte Carlo methods are often set up to be run by computers
• The computation based on the generation of appropriate random numbers
• Gradual convergence towards better estimates when more data is simulated.

Basic Parameters in the Monte Carlo Simulation

The Monte Carlo method is based on the following four steps:
• Estimates of the probabilistic distribution function of each of the input variables.
• Generation of random values for each of the parameters.
• Calculating the resistive and driving values and specifying the values of the resistive force greater than the driving force.
• Repeating these steps to the nth order and calculating the probability of collapse.

Phase2 software features
Phase2 software is a product of the Rocscience software Co. that uses a two-dimensionalfinite-element method to calculate stresses and strains around the excavated spaces (tunnels, slopes, etc.). This software can be used by mining engineers and civil engineers to provide many graphs and charts to solve substantial problems. Additionally, the effect of groundwater on the stability of structures is part of the capabilities of this software.

Other features of this software can be to examine the condition of the structure before and after adding the preservatives (shot Crete or rock bolts, etc.) and their effects and analysis of the behavior of various elements of the structure and surrounding space, and finally types of reporting.

Ability to generate random samples

This feature is used to perform the probabilistic analysis of the model.

Random samples can be material specification, model geometry, groundwater level conditions, etc.

Modeling and analysis of preservatives and amplifiers

In Phase2 software, modeling and analysis can be performed after adding a preservative and amplifier, including shot Crete and rock bolts.
The software is also capable of analyzing the strengths and stresses of the self-preserving agents.

Groundwater seepage analysis by finite element method

The Phase2 software can analyze groundwater seepage through finite-element method for a variety of saturated, unsaturated and steady states.

Demonstration of equipotential lines, flow vectors and flow network (FLOW NET)

Modeling and Analysis of Reinforced Soil Systems

Displaying the Reinforcements and Yielded Elements

Utilizing the available tool in the software, it is possible to interpret and view the results and diagrams of reinforced soil system analysis.

Finite element analysis of groundwater seepage

In the groundwater seepage analysis, it is possible to calculate the following in the software:
• Seepage analysis
• Drainage of embankment
• Combining various materials
• The phreatic level
• Separate groundwater flow calculations

Failure Zone Search

The Phase2 software is able to calculate the sliding surface in a variety of ways, including the polygon method.

Optimization of the slope angle

The software can also calculate the optimal slip surface in order to achieve the economic plan. Utilizing this function, the slope corresponding confidence coefficient is obtained.

Probabilistic analysis of slope stability

The software is capable of analyzing probabilistic problems by point estimation method. The results will be available as the probability of failure and confidence coefficient.

What you will learn in this tutorial
• Understanding the probabilistic concepts, how they are defined in software and probabilistic analysis of slopes
• Understanding the concepts of sensitivity analysis and how to perform it in software.
• Optimal slope design.
• Support and retaining design
• Modeling and Analysis of reinforced Soil Systems
• Understanding the concepts of widely used statistical and probabilistic relationships in engineering problems, especially geotechnical engineering
• Understanding the widely used probabilistic relationships such as Monte Carlo, Advanced Monte Carlo, point estimation method in geotechnical engineering
• Learn how to model underground spaces and surface drilling in the Swedge software
• Structural analysis of slop stability and formed wedges
• Seepage analysis of groundwater and its effect on slope stability

Tips and Requirements

1. Introduction to statistical concepts
2. Introduction to soil engineering concepts and relationships
3. Introduction to stone engineering concepts and relationships
4. Introduction to spreadsheets, including Microsoft Excel

Objectives of the site in presenting this project
This project is aimed at modeling and probabilistic analysis of the slope stability. This project could be helpful for university students, researchers and etc. Also it could be proved useful in scientific and industrial projects, and MSc and PhD theses. In some cases,the university students require investigation and research for their MSc and PhD theses. Since the present project consists of a complete project and includes all university flowcharts, it could prove useful.

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